As was already mentioned by several other contributors to this thread, the replies you will get here on LEO, a forum dedicated to language and populated by professional translators and proofreaders (i.e. people who make a living concentrating on the language they use, including spelling and grammar) as well as general nitpickers and grammar nerds, is not necessarily representative for German speakers as a whole.
Plus, the demographic of LEO users is probably slightly different to that of people on social networks such as Twitter or Facebook. I would hazard a guess that LEO users are older on average and that there is an above-average number of people with a university education among the regular users at least, whereas I guess on the social networks it is around the average mark.
All these factors mean that the LEO users are more likely to watch their grammar and their spelling whenever they write anything, on- or offline, be it Twitter comments, shopping lists or essays.
I am not on Twitter or Facebook (another thing you are possibly slightly more likely to read here than somewhere else, possibly also due to the demographic), so I can only speak for texting (SMS) and WhatsApp (and other such messaging apps). At least for SMS you also used to be limited to a certain number of characters, so maybe it is or at least was comparable to Twitter in that respect.
I always try to spell all words correctly, including using capital letters, and to employ the correct grammar, including punctuation. I will, however, use certain abbreviations, such as WE instead of Wochenende, Mo instead of Montag or Geb instead of Geburtstag, and if I do so I do not place a full stop behind the abbreviation. The other thing is that I often leave out the "ich" if I'm writing about myself and what I am doing, so I might text a friend "Sitze gerade im Café, war eben beim Friseur, komme gegen 5 bei Dir vorbei". A kind of shorthand, newspaper headline style, I suppose.
Oh, and I might use a colloquial/dialect expression that I wouldn't use in more formal writing, so I might write "na, wie isset?" or "Passt scho".